Short Answer:
Choking in nozzles occurs when the flow velocity at the nozzle throat (the narrowest section) reaches the speed of sound (Mach number = 1). At this condition, the flow rate becomes maximum and cannot be increased further, even if the downstream pressure is reduced.
This phenomenon happens in compressible flow, especially in gases or air flowing through converging or converging-diverging nozzles. Once choking occurs, the mass flow rate depends only on the upstream pressure and temperature and becomes independent of downstream conditions.
Detailed Explanation:
Choking in Nozzles
Choking in nozzles is a fundamental concept in compressible fluid flow, particularly in the study of gas dynamics and propulsion systems. It refers to the condition in which the flow velocity at the throat of a nozzle reaches sonic velocity (Mach 1). At this stage, the flow becomes restricted or “choked,” meaning that no additional mass flow rate can pass through the nozzle, regardless of further decreases in downstream pressure.
This phenomenon plays a vital role in the design of converging and converging-diverging nozzles, which are used in turbines, jet engines, and rockets. Understanding choking is essential for controlling and predicting the maximum flow rate and thrust performance.
Definition
Choking in nozzles is defined as the condition when the flow velocity at the throat of a nozzle becomes equal to the speed of sound (Mach number = 1), and the mass flow rate reaches its maximum possible value for the given inlet conditions.
This means the flow is limited by the sonic condition, and no additional flow can be forced through the nozzle by decreasing the back pressure.
Flow Process in a Nozzle
A nozzle is a device designed to accelerate a fluid by converting its pressure energy into kinetic energy. When a compressible fluid (like air or gas) flows through a nozzle, its velocity, pressure, and density change according to the area and pressure ratio.
- In a converging nozzle, the flow accelerates as the area decreases.
- The velocity continues to increase until it reaches the speed of sound at the throat (the narrowest point).
- Beyond this point, if the downstream pressure is reduced further, the flow cannot accelerate beyond sonic velocity at the throat. This condition is known as choked flow.
Mathematical Derivation of Choking
The mass flow rate () through a nozzle is given by:
For a compressible isentropic flow, substituting the relationships between pressure, temperature, and density gives:
where:
- = mass flow rate,
- = area of nozzle throat,
- = stagnation pressure and temperature,
- = ratio of specific heats,
- = gas constant.
The mass flow rate increases with decreasing (pressure ratio), but only up to a certain point. The maximum occurs when Mach number = 1, at which the flow is said to be choked.
At choking condition,
For air (),
This means that when the pressure ratio becomes 0.528 or lower, the flow at the throat becomes sonic and choking occurs.
Physical Meaning of Choking
When the flow becomes choked, the pressure at the throat reaches its critical value. The flow velocity cannot exceed the speed of sound because:
- Information Blockage:
- In compressible flow, pressure disturbances (sound waves) travel at the speed of sound.
- Once the flow reaches sonic speed, these disturbances cannot move upstream, preventing the system from adjusting to further pressure changes.
- Energy Limitation:
- All available energy is used to accelerate the flow to Mach 1.
- Beyond this point, additional expansion cannot increase the flow rate but only affects conditions downstream of the throat.
Thus, the mass flow rate through the nozzle remains constant even if the downstream pressure continues to drop.
Characteristics of Choked Flow
- Sonic Velocity at Throat:
- Mach number = 1 at the narrowest cross-section.
- Maximum Mass Flow Rate:
- Flow rate cannot increase further for the same upstream conditions.
- Independent of Downstream Pressure:
- After choking, lowering the back pressure does not change the mass flow rate.
- Fixed by Upstream Conditions:
- The flow rate depends only on upstream (stagnation) pressure and temperature.
- Occurs in Compressible Flow:
- Choking happens only when the gas flow is compressible (density changes with pressure).
Example
Suppose air flows through a converging nozzle with a stagnation pressure and stagnation temperature .
For air, and .
At choking, the critical pressure ratio is:
Thus,
This is the critical throat pressure, and if the back pressure drops below this value, the mass flow rate will remain unchanged.
Applications of Choking in Engineering
- Rocket and Jet Engine Nozzles:
- Determines the maximum mass flow rate of exhaust gases for thrust generation.
- Steam and Gas Turbines:
- Helps in calculating mass flow through turbine nozzles and blades.
- Venturi Flow Meters:
- Used to measure flow rates in compressible fluids under choked conditions.
- Safety Valves and Pressure Regulators:
- Ensures controlled release of gases without exceeding critical flow conditions.
- Supersonic Wind Tunnels:
- Nozzles are designed to achieve choking at the throat before expanding to supersonic speeds.
Important Notes
- Choking occurs only in compressible flows (not in incompressible liquids).
- In a converging nozzle, choking limits the flow to Mach 1.
- In a converging-diverging nozzle, once flow is choked at the throat, further expansion in the diverging section can accelerate it to supersonic speeds.
Conclusion
Choking in nozzles refers to the condition where the flow at the nozzle throat reaches sonic velocity (Mach 1) and the mass flow rate becomes maximum. Beyond this point, decreasing the downstream pressure does not increase the flow rate. It is a key concept in the analysis of compressible flow systems, such as jet engines, turbines, and nozzles, where it determines performance and efficiency. Choking helps engineers design efficient fluid flow systems by defining flow limits based on upstream conditions.